 Aims
The course aims at providing the students with conceptual bases and methods allowing them to
- solve equations in modulo integer rings;
- determine the existence conditions of solutions for certain diophantic equations;
- apply results of a mathematical analysis to the study of prime numbers;
- execute calculations in point groups of certain cubic projections on module integer bodies.
Main themes
Introduction to various aspects of the number theory and its methods, for its particular application to mathematical cryptography.
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)
Prerequisites: elements of linear algebra (first cycle level).
Evaluation: oral examination. The exam consists in the presentation of a personal work developping one aspect of numbers theory and summary questions on the overall of the course.
Support:
- K. Ireland, M. Rosen: A classical introduction to modern number theory, Springer, 2nd edition, 1991;
- J.P. Serre: Cours d'arithmetique, PUF, 1970;
- J.H. Silverman: The arithmetic of elliptic curves, Springer, 1986.
Other credits in programs
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INFO22
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Deuxième année du programme conduisant au grade d'ingénieur civil informaticien
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(3 credits)
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INFO23
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Troisième année du programme conduisant au grade d'ingénieur civil informaticien
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(3 credits)
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MAP22
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Deuxième année du programme conduisant au grade d'ingénieur civil en mathématiques appliquées
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(3 credits)
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MAP23
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Troisième année du programme conduisant au grade d'ingénieur civil en mathématiques appliquées
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(3 credits)
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MATH22/G
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Deuxième licence en sciences mathématiques
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(3 credits)
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